We propose a theoretical model that underlines the implications of a non-linear Phillips curve for the difficulty of monetary policy to fight against inflationary tensions similar to those encountered in 2021 and 2022 at a worldwide level, due to the resumption of demand after the COVID crisis and to the war in Ukraine. In such non-linearities, the interest rate becomes an asymmetric and convex function of an inflationary supply shock variation. In the case of inflationary tensions, the nominal interest rate can then strongly increase above its long-term equilibrium value. Economic recession is exacerbated, whereas inflationary tensions are more accentuated. Then, the risk is a more than proportional increase in public expenditure to compensate for the decrease in private consumption, which could not be achieved without a strong growth in the public indebtedness level.